Bent missed the 2-0 loss at Villa Park with a thigh problem and some supporters voiced their displeasure at a picture posted online of the record signing buying Christmas presents during the game.
However, Press Association Sport understands Villa are completely relaxed about the situation and are keeping their fingers crossed Bent has recovered in time to face the Gunners. Villa manager Alex McLeish said: "We can't gamble with Darren. He has to tell me he's not feeling it (the injury) and say 'I'm okay to start.'"
"Then he'll be back in the reckoning without question. He has got a thigh-cum-groin kicking strain. He came off the training pitch on Tuesday after having a shot at goal.
"When it's not a clash between two players and they pull up, it means something else has happened and it can be quite serious. But the doctor seems to think he should be quite close to being ready for Wednesday. We'll keep our fingers crossed that he is okay."
Bent reported to the club's Bodymoor Heath training ground on Sunday morning and underwent two hours of treatment. He was told by the club's doctors to go home, where he watched the majority of the Barclays Premier League clash with Liverpool on television.
It was then that Bent decided to go shopping, which led to consternation from some supporters.
Jonathan Fear, editor of the fans' website Vital Villa, told Press Association Sport: "If Darren was told to go home by the club doctors then that explains things and why he wasn't at the game.
"But even if he does care for Villa, symbolically going out shopping during the latter part of the game makes it look to the fans that he doesn't give a stuff for Villa."
Bent has already issued an apology on Twitter, which read: "Nothing is more important to me than playing football, sadly injury meant I wasn't able to do that today. Gutted not to be involved. I hope to be back very soon. Watched the majority of he game on tv. Never knew popping out would cause an issue and for that I apologise."